# Evidence of Strong Correlation between Instanton and QCD-monopole on SU(2) Lattice

## TL;DR

This paper demonstrates a strong correlation between instantons and QCD-monopoles in SU(2) lattice gauge theory, showing monopole dominance in topological charge through analytical and numerical methods.

## Contribution

It provides the first detailed analytical and numerical evidence of the correlation between instantons and QCD-monopoles in SU(2) lattice gauge theory.

## Key findings

- Monopoles penetrate instanton centers in the Polyakov gauge.
- Monopole dominance observed for topological charge in lattice simulations.
- Correlation persists in both singular and regular parts of the gauge field.

## Abstract

The correlation between instantons and QCD-monopoles is studied both in the lattice gauge theory and in the continuum theory. An analytical study in the Polyakov-like gauge, where $A_4(x)$ is diagonalized, shows that the QCD-monopole trajectory penetrates the center of each instanton, and becomes complicated in the multi-instanton system. Using the SU(2) lattice with $16^4$, the instanton number is measured in the singular (monopole-dominating) and regular (photon-dominating) parts, respectively. The monopole dominance for the topological charge is found both in the maximally abelian gauge and in the Polyakov gauge.